ُ‫کٌٌذ‬ ِ‫ارائ‬:
‫بشرگی‬ ‫سْیل‬
‫دریا‬ ‫هٌْذسی‬ ‫ارضذ‬ ‫کارضٌاسی‬
‫َّضوٌذ‬ ‫ضٌاٍرّاي‬ ‫هساتقات‬ ُ‫دٍر‬ ‫سَهیي‬
The 3nd Aut...
‫هطالة‬ ‫سزفصل‬
•‫ّا‬ ‫آى‬ ‫ّای‬ ‫ٍيژگی‬ ٍ ‫دريايی‬ ‫ّای‬ ُ‫پیشبزًذ‬ ‫اًَاع‬ ‫هعزفی‬
•‫دريايی‬ ‫ّای‬ ًِ‫پزٍا‬ ‫عولکزد‬ ‫در...
‫ّا‬ ُ‫پیطثزًذ‬ ‫اًَاع‬
• Propellers
– Fixed Pitch
– Controllable (Reversible) Pitch
– CRP
– Super Cavitating
– Ducted
– V...
‫هشايا‬
•‫بز‬ ‫هختلف‬ ‫ّای‬ ‫سزعت‬ ‫تا‬ ‫باال‬ ‫راًذهاى‬
‫ًَع‬ ‫حسب‬
•‫کن‬ ٌِ‫ّشي‬
‫هعايب‬
-‫هحذٍد‬ ‫عولیاتی‬ ‫شزايط‬ ‫در‬...
‫هشايا‬
•ُ‫دًذ‬ ِ‫جعب‬ ِ‫ب‬ ‫ًیاس‬ ‫بذٍى‬ ‫عقب‬ ِ‫ب‬ ٍ‫ر‬ ‫تزاست‬
•‫ٍسیع‬ ‫عولکزد‬ ُ‫هحذٍد‬
•‫هختلف‬ ‫ّای‬ ‫سزعت‬ ‫در‬ ‫هَ...
‫گزد‬ ‫هعکَس‬ ‫ّای‬ ًِ‫پزٍا‬Contra-Rotating Propellers
+‫گشتاٍر‬ ‫در‬ ‫تعادل‬
+‫باال‬ ‫راًذهاى‬
+‫کن‬ ‫ًَيش‬ ٍ ‫ارتعاشات‬
...
‫هغزٍق‬ ِ‫ًیو‬ ‫ّای‬ ًِ‫پزٍا‬
•‫تاال‬ ‫سزعتْاي‬ ‫در‬ ‫تاال‬ ‫راًص‬ ‫راًذهاى‬
•‫هلحقات‬ ‫درگ‬ ‫کاّص‬
•‫تشرگتز‬ ‫ّاي‬ ًِ‫پزٍ...
‫جت‬ ‫ٍاتز‬(‫آب‬ ‫جت‬)
•‫هشایا‬:
•‫تاال‬ ‫ّاي‬ ‫سزعت‬ ‫در‬ ‫تاال‬ ‫راًذهاى‬
•‫عوق‬ ‫کن‬ ‫آب‬ ‫در‬ ‫عولکزد‬ ‫قاتلیت‬
•‫تاال...
‫ّا‬ ُ‫پیطثزًذ‬ ‫اًَاع‬ ِ‫هقایس‬
9
ًِ‫پزٍا‬ ‫هطخصات‬
• Blade
– Tip
– Root
– Leading Edge
– Trailing Edge
– Pitch Angle
– Angle of Attack
 Diameter
 Pitch
...
ُ‫پز‬ ‫ٌّذسی‬ ‫هطخصات‬
11
‫پروانه‬ ‫گام‬
12
ًِ‫پزٍا‬ ‫سطَح‬
13
َ‫اسکی‬
The best practical option for reducing
unsteady flow forces on the propeller,
and thus reducing vibration is to sk...
ِ‫تطات‬ ‫اصَل‬
• Dimensional analysis:
• Result is:
15
‫هذل‬ ‫تست‬ ‫در‬ ‫تٌذي‬ ‫هقیاس‬ ‫قَاًیي‬
• Introduce the scale ratio:
• Froude scaling results in:
• nD/VA equality result...
‫هذل‬ ‫تست‬ ‫در‬ ‫تٌذي‬ ‫هقیاس‬ ‫قَاًیي‬
17
ًِ‫پزٍا‬ ‫ضزایة‬
18
ًِ‫پزٍا‬ ‫عولکزدي‬ ‫ّاي‬ ‫هٌحٌی‬
19
ًِ‫تذ‬ ‫اًذرکٌص‬-ًِ‫پزٍا‬
• Wake
• Slip ratio
• Relative Rotative Efficiency
• Thrust deduction
• Hull efficiency
• Propul...
‫ویک‬
• The difference between the ship speed V and the speed of advance VA is the wake
speed.The wake fraction is defined...
‫ًسثی‬ ‫چزخص‬ ‫راًذهاى‬
open water propeller efficiency and efficiency behind the hull:
Their ratio is called the relative...
‫تزاست‬ ‫کاّص‬ ‫ضزیة‬
When a hull is towed, there is an area of high pressure over the stern which has
a resultant forward...
ًِ‫تذ‬ ‫راًذهاى‬
The work done in moving a ship at a speed V against a resistance R is proportional to the
product RV or t...
‫رانش‬ ‫کل‬ ‫راندمان‬
• Need to select a propeller such that hP is maximized.
25
‫هطالة‬ ‫هزٍر‬
• Thrust Coefficient (KT)
• Torque Coefficient (KQ)
• Advance Coefficient (J)
• Open-water Propeller Effici...
‫کاٍیتاسیَى‬
• Cavitation occurs when pressure on back or suction side of blade
becomes so low that water vaporizes and va...
ًِ‫پزٍا‬ ‫کاٍیتاسیَى‬
• Sheet
• Bubble
• Cloud
• Tip and Hub Vortex
28
‫کاٍیتاسیَى‬ ‫کاّص‬ ‫ّاي‬ ‫رٍش‬
• Must sufficient blade area
• Sufficient hub immersion
• Burrill Cavitation Diagram
• Kel...
Keller Criterion
 
 
A
A
Z T
p p D
k
E
O o v




13 0 3
2
. .
Where:
T = Thrust, N
Z = Number of Blades
p - p = Pr...
Burrill Cavitation Diagram
2 2 2
A
2 2
188.2+19.62h
0.7 V 4.836
( / )
0.5 [ (0.7 ) ]
Diagram gives the local
cavitation nu...
ًِ‫پزٍا‬ ‫استاًذارد‬ ‫ّاي‬ ‫سزي‬
• Open water tests of geometrically related propellers with pitch and other
variables var...
‫سزي‬ ًِ‫پزٍا‬ ‫ًوَدارّاي‬B-Wageningen
33
ًِ‫پزٍا‬ ‫طزاحی‬ ‫هالحظات‬
• Inputs:
– Design speed
– Diameter constraints
– EHP at design speed
– Type and number of prop...
‫تزاست‬ ‫ضزیة‬ ‫طزیق‬ ‫اس‬ ‫ثاتت‬ ‫قطز‬ ‫تا‬ ‫طزاحی‬
Case 1: From the hull requirements we might have a required ship spee...
‫سزي‬ ‫طزاحی‬ ‫ًوَدارّاي‬ ‫اس‬ ‫اي‬ ًَِ‫ًو‬B-Wageningen
36
‫گطتاٍر‬ ‫ضزیة‬ ‫طزیق‬ ‫اس‬ ‫ثاتت‬ ‫قطز‬ ‫تا‬ ‫طزاحی‬
Case 2: From the engine requirements we might have a delivered power...
‫تزاست‬ ‫ضزیة‬ ‫طزیق‬ ‫اس‬ ِ‫ت‬ ‫ثاتت‬ ‫دٍر‬ ‫تا‬ ‫طزاحی‬
Case 1: From the hull requirements we might have a required ship...
‫گطتاٍر‬ ‫ضزیة‬ ‫طزیق‬ ‫اس‬ ِ‫ت‬ ‫ثاتت‬ ‫دٍر‬ ‫تا‬ ‫طزاحی‬
Case 2: From the engine requirements we might have a required s...
‫سزٍیس‬ ‫حالت‬ ‫در‬ ‫هَتَر‬ ‫ًیاس‬ ‫هَرد‬ ‫قذرت‬
• To maintain contracted design speed on average over ship’s service life...
‫جت‬ ‫ٍاتز‬
 
 
jet jet 2
2 21
jet2
Basic variables and assumptions:
Ship speed , Resistance
Water jet diameter .
100%...
‫ضفت‬ ‫تٌذي‬ ‫آب‬
42
‫شما‬ ‫توجه‬ ‫و‬ ‫حضور‬ ‫از‬ ‫تشکر‬ ‫با‬
43
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Transcript of "Propulsion%20system %203rd[1]"

  1. 1. ُ‫کٌٌذ‬ ِ‫ارائ‬: ‫بشرگی‬ ‫سْیل‬ ‫دریا‬ ‫هٌْذسی‬ ‫ارضذ‬ ‫کارضٌاسی‬ ‫َّضوٌذ‬ ‫ضٌاٍرّاي‬ ‫هساتقات‬ ُ‫دٍر‬ ‫سَهیي‬ The 3nd Autonomous Surface Vehicle Competition ُ‫کٌٌذ‬ ‫بزگشار‬: ‫شزيف‬ ‫صٌعتی‬ ُ‫داًشگا‬ ‫دريا‬ ‫هٌْذسی‬ ‫اًجوي‬ ‫خذا‬ ‫ًام‬ ِ‫ب‬ 1
  2. 2. ‫هطالة‬ ‫سزفصل‬ •‫ّا‬ ‫آى‬ ‫ّای‬ ‫ٍيژگی‬ ٍ ‫دريايی‬ ‫ّای‬ ُ‫پیشبزًذ‬ ‫اًَاع‬ ‫هعزفی‬ •‫دريايی‬ ‫ّای‬ ًِ‫پزٍا‬ ‫عولکزد‬ ‫در‬ ‫هَثز‬ ‫پاراهتزّای‬ ‫هعزفی‬ •‫طزاحی‬ ِ‫ًقط‬ ِ‫ب‬ ِ‫تَج‬ ‫با‬ ًِ‫پزٍا‬ ‫طزاحی‬ ‫پاراهتزّای‬ ‫تعییي‬ 2
  3. 3. ‫ّا‬ ُ‫پیطثزًذ‬ ‫اًَاع‬ • Propellers – Fixed Pitch – Controllable (Reversible) Pitch – CRP – Super Cavitating – Ducted – Vertical Axis • Jet – Water jet – Pump jet • Podded Propulsion 3
  4. 4. ‫هشايا‬ •‫بز‬ ‫هختلف‬ ‫ّای‬ ‫سزعت‬ ‫تا‬ ‫باال‬ ‫راًذهاى‬ ‫ًَع‬ ‫حسب‬ •‫کن‬ ٌِ‫ّشي‬ ‫هعايب‬ -‫هحذٍد‬ ‫عولیاتی‬ ‫شزايط‬ ‫در‬ ‫کارکزد‬ ‫قابلیت‬ ‫ثاتت‬ ‫گام‬ ‫تا‬ ‫ّاي‬ ًِ‫پزٍا‬(FPP) 4
  5. 5. ‫هشايا‬ •ُ‫دًذ‬ ِ‫جعب‬ ِ‫ب‬ ‫ًیاس‬ ‫بذٍى‬ ‫عقب‬ ِ‫ب‬ ٍ‫ر‬ ‫تزاست‬ •‫ٍسیع‬ ‫عولکزد‬ ُ‫هحذٍد‬ •‫هختلف‬ ‫ّای‬ ‫سزعت‬ ‫در‬ ‫هَتَر‬ ‫با‬ ‫بْتز‬ ‫ساسگاری‬ •‫شٌاٍر‬ ‫پذيزی‬ ‫هاًَر‬ ‫افشايش‬ ‫هعايب‬ ِ‫ب‬ ‫ًسبت‬ ‫کوتز‬ ‫راًذهاى‬F.P.P ‫ساختار‬ ‫پیچیذگی‬ ‫باال‬ ٌِ‫ّشي‬ ‫هتغیز‬ ‫گام‬ ‫تا‬ ‫ّاي‬ ًِ‫پزٍا‬(CPP) 5
  6. 6. ‫گزد‬ ‫هعکَس‬ ‫ّای‬ ًِ‫پزٍا‬Contra-Rotating Propellers +‫گشتاٍر‬ ‫در‬ ‫تعادل‬ +‫باال‬ ‫راًذهاى‬ +‫کن‬ ‫ًَيش‬ ٍ ‫ارتعاشات‬ -‫باال‬ ٌِ‫ّشي‬ ٍ ‫پیچیذگی‬ 6
  7. 7. ‫هغزٍق‬ ِ‫ًیو‬ ‫ّای‬ ًِ‫پزٍا‬ •‫تاال‬ ‫سزعتْاي‬ ‫در‬ ‫تاال‬ ‫راًص‬ ‫راًذهاى‬ •‫هلحقات‬ ‫درگ‬ ‫کاّص‬ •‫تشرگتز‬ ‫ّاي‬ ًِ‫پزٍا‬ ‫اس‬ ُ‫استفاد‬ ‫اهکاى‬ •‫اس‬ ‫ًاضی‬ ُ‫پز‬ ‫سطح‬ ‫سایطی‬ ‫خَردگی‬ ‫کاّص‬ ‫کاٍیتاسیَى‬ -‫ارتعاضات‬ ‫افشایص‬ -‫تاال‬ ٌِ‫ٍّشی‬ ‫پیچیذگی‬ -‫ضذیذ‬ ‫ًَساًی‬ ‫تارگذاري‬ ‫هعزض‬ ‫در‬ 7
  8. 8. ‫جت‬ ‫ٍاتز‬(‫آب‬ ‫جت‬) •‫هشایا‬: •‫تاال‬ ‫ّاي‬ ‫سزعت‬ ‫در‬ ‫تاال‬ ‫راًذهاى‬ •‫عوق‬ ‫کن‬ ‫آب‬ ‫در‬ ‫عولکزد‬ ‫قاتلیت‬ •‫تاال‬ ‫هاًَرپذیزي‬ ‫هعایة‬: •‫تاال‬ ٌِ‫ّشی‬ •‫ًگْذاري‬ ٍ ‫تعویز‬ ‫هطکالت‬ 8
  9. 9. ‫ّا‬ ُ‫پیطثزًذ‬ ‫اًَاع‬ ِ‫هقایس‬ 9
  10. 10. ًِ‫پزٍا‬ ‫هطخصات‬ • Blade – Tip – Root – Leading Edge – Trailing Edge – Pitch Angle – Angle of Attack  Diameter  Pitch  Skew  Rake  Area  Slip  Thrust 10
  11. 11. ُ‫پز‬ ‫ٌّذسی‬ ‫هطخصات‬ 11
  12. 12. ‫پروانه‬ ‫گام‬ 12
  13. 13. ًِ‫پزٍا‬ ‫سطَح‬ 13
  14. 14. َ‫اسکی‬ The best practical option for reducing unsteady flow forces on the propeller, and thus reducing vibration is to skew the blades. The mid radius of a skewed propeller is in the same place as that of a conventional radial propeller, but the relationship between inner and outer radius is shifted, the tip hits it later and there follows a cancellation of forces. A skewed propeller can be “tuned” to a specific wake field in order to reduce the excitation at a given harmonic, and thus be very effective in reducing vibration. 14
  15. 15. ِ‫تطات‬ ‫اصَل‬ • Dimensional analysis: • Result is: 15
  16. 16. ‫هذل‬ ‫تست‬ ‫در‬ ‫تٌذي‬ ‫هقیاس‬ ‫قَاًیي‬ • Introduce the scale ratio: • Froude scaling results in: • nD/VA equality results in slip ratio equality. • The third coefficient cannot be made equal unless we adjust the ambient pressure - cavitation tests. • The fourth coefficient (Reynolds number) cannot be made equal. This is not as serious as for resistance. 16
  17. 17. ‫هذل‬ ‫تست‬ ‫در‬ ‫تٌذي‬ ‫هقیاس‬ ‫قَاًیي‬ 17
  18. 18. ًِ‫پزٍا‬ ‫ضزایة‬ 18
  19. 19. ًِ‫پزٍا‬ ‫عولکزدي‬ ‫ّاي‬ ‫هٌحٌی‬ 19
  20. 20. ًِ‫تذ‬ ‫اًذرکٌص‬-ًِ‫پزٍا‬ • Wake • Slip ratio • Relative Rotative Efficiency • Thrust deduction • Hull efficiency • Propulsive efficiency 20
  21. 21. ‫ویک‬ • The difference between the ship speed V and the speed of advance VA is the wake speed.The wake fraction is defined as: • w = (V −VA) / V so VA = V (1 −w ) ‫اي‬ ًِ‫پزٍا‬ ‫تک‬: ‫اي‬ ًِ‫پزٍا‬ ٍ‫د‬: 21 05.0C45.0w)Robertson( 8.0C7.0w)Heckscher( C5.005.0w)Taylor( p p B    2.0C5.0w)Robertson( 3.0C7.0w)Heckscher( C55.02.0w)Taylor( p p B   
  22. 22. ‫ًسثی‬ ‫چزخص‬ ‫راًذهاى‬ open water propeller efficiency and efficiency behind the hull: Their ratio is called the relative rotative efficiency: 0.95 -1.0 for twin screw ships 1.0 - 1.1 for single screw. 22
  23. 23. ‫تزاست‬ ‫کاّص‬ ‫ضزیة‬ When a hull is towed, there is an area of high pressure over the stern which has a resultant forward component reducing the total resistance. With a self propelled hull, however, the pressure over some of this area is reduced by the action of the propeller in accelerating the water flowing into it, the forward component is reduced, the resistance is increased and so is the thrust necessary to propel the model or ship. If R is the resistance and T the thrust, we can write for the same ship speed where the expression (1-t) is called the thrust deduction factor . 23
  24. 24. ًِ‫تذ‬ ‫راًذهاى‬ The work done in moving a ship at a speed V against a resistance R is proportional to the product RV or the effective power PE. The work done by the propeller in delivering a thrust T at a speed of advance VA is proportional to the product TVA or the thrust power P. The ratio of the work done on the ship with that done by the propeller is called the hull efficiency For most ships this is greater than 1. At first sight this seems an anomalous situation in that apparently something is being obtained for nothing. It can,however, be explained by the fact that the propeller is making use of the energy which is already in the wake because of its forward velocity. 24
  25. 25. ‫رانش‬ ‫کل‬ ‫راندمان‬ • Need to select a propeller such that hP is maximized. 25
  26. 26. ‫هطالة‬ ‫هزٍر‬ • Thrust Coefficient (KT) • Torque Coefficient (KQ) • Advance Coefficient (J) • Open-water Propeller Efficiency (h0) • Pitch-diameter ratio (P/D) • Expanded area ratio (AE/A0) • Thrust deduction, t • Wake fraction, w • Speed of advance, VA VwV TtR K KJ nQ TV nD V J Dn Q K Dn T K A Q TA A Q T )1( )1( 22 0 52 42        h   26
  27. 27. ‫کاٍیتاسیَى‬ • Cavitation occurs when pressure on back or suction side of blade becomes so low that water vaporizes and vapor-filled cavities of bubbles form. • Occurs on heavily loaded propellers • high rotational speed Bubbles can collapse on blades and cause: • erosion • serious noise problems • rapid decrease in propeller efficiency • fluctuating forces that give rise to severe vibrations 27
  28. 28. ًِ‫پزٍا‬ ‫کاٍیتاسیَى‬ • Sheet • Bubble • Cloud • Tip and Hub Vortex 28
  29. 29. ‫کاٍیتاسیَى‬ ‫کاّص‬ ‫ّاي‬ ‫رٍش‬ • Must sufficient blade area • Sufficient hub immersion • Burrill Cavitation Diagram • Keller Criterion. 29
  30. 30. Keller Criterion     A A Z T p p D k E O o v     13 0 3 2 . . Where: T = Thrust, N Z = Number of Blades p - p = Pressure at propeller centerline (N / m ) k = Constant varying from 0 for transom - stern naval vessels to 0.20 for high - powered single screw vessels o v 2 30
  31. 31. Burrill Cavitation Diagram 2 2 2 A 2 2 188.2+19.62h 0.7 V 4.836 ( / ) 0.5 [ (0.7 ) ] Diagram gives the local cavitation number = versus the mean thrust blade loading .P A R n D T A c V nD       2 is the head of the water (m), the propeller diameter (m), is revolutions per second, the speed of advance (m/sec), T the thrust (kN), and the projected blade area (m ). This is related to t A P h D n V A he more commonly used developed area by the following approximate formula 1.067 0.229 .P D D A P A D A   31
  32. 32. ًِ‫پزٍا‬ ‫استاًذارد‬ ‫ّاي‬ ‫سزي‬ • Open water tests of geometrically related propellers with pitch and other variables varied systematically. • Thrust, torque coefficients and open water efficiency measured and plotted versus speed of advance. • Comprehensive series, such as B –Wageningen&Gawn series. 32
  33. 33. ‫سزي‬ ًِ‫پزٍا‬ ‫ًوَدارّاي‬B-Wageningen 33
  34. 34. ًِ‫پزٍا‬ ‫طزاحی‬ ‫هالحظات‬ • Inputs: – Design speed – Diameter constraints – EHP at design speed – Type and number of propellers (skew angle, blades, etc.). – Wake fraction (w) and thrust deduction (t) • Approach – Select number of blades based on frequency of excitation (similar designs). – Select area ratio based on cavitation limitations – The minimum area ratio allowed by cavitation or strength will have the best efficiency. – In general, larger diameter is better. – In general, lower RPM is better. – If machinery sets RPM, then seek the optimum diameter. 34
  35. 35. ‫تزاست‬ ‫ضزیة‬ ‫طزیق‬ ‫اس‬ ‫ثاتت‬ ‫قطز‬ ‫تا‬ ‫طزاحی‬ Case 1: From the hull requirements we might have a required ship speed and resistance: – Select a blade number. – Select a minimum acceptable AE/A0. – Work with KT and J. – Form the ratio KT/J2 to eliminate the unknown n. – Optimize for maximum open water propeller efficiency. 35
  36. 36. ‫سزي‬ ‫طزاحی‬ ‫ًوَدارّاي‬ ‫اس‬ ‫اي‬ ًَِ‫ًو‬B-Wageningen 36
  37. 37. ‫گطتاٍر‬ ‫ضزیة‬ ‫طزیق‬ ‫اس‬ ‫ثاتت‬ ‫قطز‬ ‫تا‬ ‫طزاحی‬ Case 2: From the engine requirements we might have a delivered power and ship speed:  Select a blade number.  Select a minimum acceptable AE/A0.  Work with KQ and J.  Form the ratio KQ/J3 to eliminate the unknown n.  Optimize for maximum open water propeller efficiency. 37
  38. 38. ‫تزاست‬ ‫ضزیة‬ ‫طزیق‬ ‫اس‬ ِ‫ت‬ ‫ثاتت‬ ‫دٍر‬ ‫تا‬ ‫طزاحی‬ Case 1: From the hull requirements we might have a required ship speed and resistance: • Select a blade number. • Select a minimum acceptable AE/A0. Iterations may be necessary since some cavitation criteria involve the diameter D. • Work with KT and J. • Form the ratio KT/J4 to eliminate the unknown D. • Optimize for maximum open water propeller efficiency. 38
  39. 39. ‫گطتاٍر‬ ‫ضزیة‬ ‫طزیق‬ ‫اس‬ ِ‫ت‬ ‫ثاتت‬ ‫دٍر‬ ‫تا‬ ‫طزاحی‬ Case 2: From the engine requirements we might have a required ship speed and delivered power: • Select a blade number. • Select a minimum acceptable AE/A0. Iteration may be necessary since some cavitation criteria involve the diameter D. • Work with KQ and J. • Form the ratio KQ/J5 to eliminate the unknown D. • Optimize for maximum open water propeller efficiency. 39
  40. 40. ‫سزٍیس‬ ‫حالت‬ ‫در‬ ‫هَتَر‬ ‫ًیاس‬ ‫هَرد‬ ‫قذرت‬ • To maintain contracted design speed on average over ship’s service life in actual sea conditions (referred to as “sustained speed” by USN), installed power must be greater than PS. • A service power allowance is added, expressed as fraction of PS. • USN determines sustained speed at 80% of maximum continuous installed power. • This covers added resistance due to sea waves. 21 February 2002 Propellers 40
  41. 41. ‫جت‬ ‫ٍاتز‬     jet jet 2 2 21 jet2 Basic variables and assumptions: Ship speed , Resistance Water jet diameter . 100% efficient pumping system. Basic equations: , / 4 Power in: Power out: Pow Efficiency: V R D Q R Q V V V D Q V V RV            jet 2 21 jetjet2 er out 2 Power in Efficiency goes down as becomes smaller. Q V V V V V VQ V V V       41
  42. 42. ‫ضفت‬ ‫تٌذي‬ ‫آب‬ 42
  43. 43. ‫شما‬ ‫توجه‬ ‫و‬ ‫حضور‬ ‫از‬ ‫تشکر‬ ‫با‬ 43
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